He is now in a phase where he doesn't poop for more than a week.
What was his pattern before?
The purpose of the large bowel is to remove water from food waste. The longer it sits inside, the drier and harder it gets. Having a BM weekly may be painful. That may keep him from straining and doing it. Avoiding BMs=> drier harder, painful => avoiding BMs.
Is he having pain? Is he having liquid or hard BMs? IF liquid, this is fecal impaction and needs specific management. If he has a doc, mention it. He may need a rectal exam to tell for sure what's going on.
Bottom line (no pun intended!) he will probably be more comfortable with more frequent, softer BMs. The trick with this is to not delay. When he gets the urge to have a BM, have him do it sooner rather than later. But bottom line--If he's not having pain or difficulty with BMs, don't worry about it!
If there's some fruit he likes push that (what 2-3 yo ISN'T a picky eater?) And btw, many kids in that age range suddenly eat much less. Half a sandwich and a half a glass of milk is all they eat all day, and that's normal. Fluoride vitamin is still a good idea.
More fruit and vegetables, other fiber may help.
If he's not having pain or difficulty with BMs, don't worry about it.
(For the kid WITH pain and or difficulty, or liquid stool around a big blob in the rectum..) Often, starting with oil retention or a Fleet's enema will 'reset' the rectum and let him go back to more frequent BMs.
There are rare conditions that can cause constipation but the most common is avoiding BMs=> drier harder, painful => avoiding BMs.
Plus too little fruit, vegetables and other fiber in diet. But bottom line--If he's not having pain or difficulty with BMs, don't worry about it!